Graduate Thesis Or Dissertation

Wavepacket-Mean Flow Interactions in the Kadomtsev–Petviashvili Equation

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https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/sj139387f
Abstract
  • The interaction between a two-dimensional, vanishing amplitude (linear) wavepacket and a nonlinear, one-dimensional expansion wave is analyzed. Utilizing wave modulation theory in which the wavepacket’s oscillation period is much shorter than the total evolution time, approximate solutions are found to the governing partial differential equation, the Kadomtsev-Petviashvili (KP) equation, which models a variety of nonlinear wave phenomena. The conditions on the incident wavepacket’s wave vector that lead to either trapping or transmission of the wavepacket by the background mean flow are analyzed, and the evolution of the wavepacket amplitude is also determined. These solutions of the two-dimensional KP-Whitham modulation system in the harmonic limit are compared to analogous solutions of the one-dimensional Korteweg-deVries-Whitham modulation system.

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  • 2025-04-23
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  • 2025-07-24
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